\documentclass[9pt]{article}
\usepackage{amsmath}
\begin{document}
Read in the following dictionary:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  74.0 & -5.00 x_{1} & -6.00 x_{2} & -3.00 x_{3} & +  1.00 x_{4} & -7.00 x_{5} & -8.00 x_{6} & -9.00 x_{7} & -3.00 x_{8} & -5.00 x_{9}\\
 x_{11}   &  -31.0 & +  3.00 x_{1} & +  8.00 x_{2} & -3.00 x_{3} & +  6.00 x_{4} & -1.00 x_{5} & +  5.00 x_{6} & +  2.00 x_{7} & +  5.00 x_{8} & -10.00 x_{9}\\
 x_{12}   &  -60.0 & +  4.00 x_{1} & +  2.00 x_{2} & +  5.00 x_{3} & +  1.00 x_{4} & +  2.00 x_{5} & + 10.00 x_{6} & + 10.00 x_{7} & -10.00 x_{8} & +  2.00 x_{9}\\
 x_{13}   &  11.0 & +  4.00 x_{1} & -5.00 x_{2} & -1.00 x_{3} & +  3.00 x_{4} & -8.00 x_{5} & -7.00 x_{6} & +  5.00 x_{7} & -7.00 x_{8} & +  6.00 x_{9}\\
 x_{14}   &  -11.0 & +  6.00 x_{1} & -2.00 x_{2} & +  7.00 x_{3} & -9.00 x_{4} & + 10.00 x_{5} &   & -8.00 x_{7} & +  5.00 x_{8} & -2.00 x_{9}\\
 x_{15}   &  1.0 & -7.00 x_{1} & +  3.00 x_{2} & -5.00 x_{3} & +  3.00 x_{4} & -2.00 x_{5} & + 10.00 x_{6} & +  5.00 x_{7} & -2.00 x_{8} & +  3.00 x_{9}\\
 x_{16}   &  -11.0 & +  8.00 x_{1} & +  1.00 x_{2} &   & -1.00 x_{4} & +  8.00 x_{5} & +  2.00 x_{6} & -6.00 x_{7} & -4.00 x_{8} & -6.00 x_{9}\\
 x_{17}   &  -22.0 & -3.00 x_{1} & +  4.00 x_{2} & +  5.00 x_{3} & +  4.00 x_{4} & +  5.00 x_{5} & -7.00 x_{6} & + 10.00 x_{7} & -7.00 x_{8} & -4.00 x_{9}\\
\hline
z    &  0.0  &   & +  4.00 x_{2} & -5.00 x_{3} & +  4.00 x_{4} & +  1.00 x_{5} &   & +  2.00 x_{7} & -5.00 x_{8} & +  2.00 x_{9}\\
\end{array}\]
\subsection{Initialization Phase: Dual Problem Solving}
New Objective in primal was changed to : \[ \max\ \sum_{j=1}^{9}\ - x_j \] 
Primal variable $x_j$ corresponds to dual variable $y_j$ for $j = 1,\ldots,17$
Dual Dictionary (with objective changed is): 
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  1.0 & +  5.00 y_{10} & -3.00 y_{11} & -4.00 y_{12} & -4.00 y_{13} & -6.00 y_{14} & +  7.00 y_{15} & -8.00 y_{16} & +  3.00 y_{17}\\
 y_{2}   &  1.0 & +  6.00 y_{10} & -8.00 y_{11} & -2.00 y_{12} & +  5.00 y_{13} & +  2.00 y_{14} & -3.00 y_{15} & -1.00 y_{16} & -4.00 y_{17}\\
 y_{3}   &  1.0 & +  3.00 y_{10} & +  3.00 y_{11} & -5.00 y_{12} & +  1.00 y_{13} & -7.00 y_{14} & +  5.00 y_{15} &   & -5.00 y_{17}\\
 y_{4}   &  1.0 & -1.00 y_{10} & -6.00 y_{11} & -1.00 y_{12} & -3.00 y_{13} & +  9.00 y_{14} & -3.00 y_{15} & +  1.00 y_{16} & -4.00 y_{17}\\
 y_{5}   &  1.0 & +  7.00 y_{10} & +  1.00 y_{11} & -2.00 y_{12} & +  8.00 y_{13} & -10.00 y_{14} & +  2.00 y_{15} & -8.00 y_{16} & -5.00 y_{17}\\
 y_{6}   &  1.0 & +  8.00 y_{10} & -5.00 y_{11} & -10.00 y_{12} & +  7.00 y_{13} &   & -10.00 y_{15} & -2.00 y_{16} & +  7.00 y_{17}\\
 y_{7}   &  1.0 & +  9.00 y_{10} & -2.00 y_{11} & -10.00 y_{12} & -5.00 y_{13} & +  8.00 y_{14} & -5.00 y_{15} & +  6.00 y_{16} & -10.00 y_{17}\\
 y_{8}   &  1.0 & +  3.00 y_{10} & -5.00 y_{11} & + 10.00 y_{12} & +  7.00 y_{13} & -5.00 y_{14} & +  2.00 y_{15} & +  4.00 y_{16} & +  7.00 y_{17}\\
 y_{9}   &  1.0 & +  5.00 y_{10} & + 10.00 y_{11} & -2.00 y_{12} & -6.00 y_{13} & +  2.00 y_{14} & -3.00 y_{15} & +  6.00 y_{16} & +  4.00 y_{17}\\
\hline
z    &  -0 & -74.00 y_{10} & + 31.00 y_{11} & + 60.00 y_{12} & -11.00 y_{13} & + 11.00 y_{14} & -1.00 y_{15} & + 11.00 y_{16} & + 22.00 y_{17}\\
\end{array}\]
Initialization succeeded in finding final dual dictionary with 6 pivots
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{14}   &  0.075275839549 & +  0.34 y_{10} & +  0.00 y_{2} & +  0.02 y_{6} & +  0.02 y_{7} & -0.07 y_{1} & +  0.87 y_{15} & -0.96 y_{16} & -0.05 y_{5}\\
 y_{11}   &  0.10299728457 & +  0.41 y_{10} & -0.11 y_{2} & +  0.02 y_{6} & +  0.02 y_{7} & -0.07 y_{1} & +  0.36 y_{15} & -0.46 y_{16} & +  0.03 y_{5}\\
 y_{3}   &  0.112226308734 & -3.90 y_{10} & -0.45 y_{2} & -0.01 y_{6} & +  0.36 y_{7} & +  0.23 y_{1} & +  2.16 y_{15} & +  5.29 y_{16} & +  0.76 y_{5}\\
 y_{4}   &  0.755989413261 & -2.33 y_{10} & +  0.74 y_{2} & -0.18 y_{6} & +  0.25 y_{7} & -0.02 y_{1} & -0.06 y_{15} & -4.61 y_{16} & -0.54 y_{5}\\
 y_{17}   &  0.0478981198226 & +  0.35 y_{10} & -0.03 y_{2} & +  0.04 y_{6} & -0.04 y_{7} & +  0.01 y_{1} & +  0.20 y_{15} & +  0.03 y_{16} & -0.04 y_{5}\\
 y_{12}   &  0.0876843226893 & +  0.78 y_{10} & +  0.05 y_{2} & -0.05 y_{6} & -0.05 y_{7} & -0.01 y_{1} & -0.48 y_{15} & -0.04 y_{16} & -0.02 y_{5}\\
 y_{13}   &  0.00807754442649 & -0.09 y_{10} & +  0.01 y_{2} & +  0.04 y_{6} & -0.02 y_{7} & -0.08 y_{1} & +  0.80 y_{15} & -0.14 y_{16} & +  0.03 y_{5}\\
 y_{8}   &  1.37730725604 & +  8.92 y_{10} & +  0.92 y_{2} & -0.13 y_{6} & -1.04 y_{7} & +  0.07 y_{1} & -1.92 y_{15} & +  9.94 y_{16} & -0.19 y_{5}\\
 y_{9}   &  2.14828309215 & + 10.14 y_{10} & -1.41 y_{2} & +  0.29 y_{6} & +  0.32 y_{7} & -0.28 y_{1} & -0.68 y_{15} & +  0.54 y_{16} & -0.06 y_{5}\\
\hline
z    &  10.2469150655 & -1.98 y_{10} & -1.44 y_{2} & -1.68 y_{6} & -2.61 y_{7} & -2.58 y_{1} & -13.25 y_{15} & -14.23 y_{16} & -1.93 y_{5}\\
\end{array}\]
Primal Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  1.98112948132 & -0.34 x_{14} & -0.41 x_{11} & +  3.90 x_{3} & +  2.33 x_{4} & -0.35 x_{17} & -0.78 x_{12} & +  0.09 x_{13} & -8.92 x_{8} & -10.14 x_{9}\\
 x_{2}   &  1.44323376757 & -0.00 x_{14} & +  0.11 x_{11} & +  0.45 x_{3} & -0.74 x_{4} & +  0.03 x_{17} & -0.05 x_{12} & -0.01 x_{13} & -0.92 x_{8} & +  1.41 x_{9}\\
 x_{6}   &  1.68076513251 & -0.02 x_{14} & -0.02 x_{11} & +  0.01 x_{3} & +  0.18 x_{4} & -0.04 x_{17} & +  0.05 x_{12} & -0.04 x_{13} & +  0.13 x_{8} & -0.29 x_{9}\\
 x_{7}   &  2.61129825044 & -0.02 x_{14} & -0.02 x_{11} & -0.36 x_{3} & -0.25 x_{4} & +  0.04 x_{17} & +  0.05 x_{12} & +  0.02 x_{13} & +  1.04 x_{8} & -0.32 x_{9}\\
 x_{1}   &  2.58483140274 & +  0.07 x_{14} & +  0.07 x_{11} & -0.23 x_{3} & +  0.02 x_{4} & -0.01 x_{17} & +  0.01 x_{12} & +  0.08 x_{13} & -0.07 x_{8} & +  0.28 x_{9}\\
 x_{15}   &  13.2464510363 & -0.87 x_{14} & -0.36 x_{11} & -2.16 x_{3} & +  0.06 x_{4} & -0.20 x_{17} & +  0.48 x_{12} & -0.80 x_{13} & +  1.92 x_{8} & +  0.68 x_{9}\\
 x_{16}   &  14.2299178497 & +  0.96 x_{14} & +  0.46 x_{11} & -5.29 x_{3} & +  4.61 x_{4} & -0.03 x_{17} & +  0.04 x_{12} & +  0.14 x_{13} & -9.94 x_{8} & -0.54 x_{9}\\
 x_{5}   &  1.92678651222 & +  0.05 x_{14} & -0.03 x_{11} & -0.76 x_{3} & +  0.54 x_{4} & +  0.04 x_{17} & +  0.02 x_{12} & -0.03 x_{13} & +  0.19 x_{8} & +  0.06 x_{9}\\
\hline
z    &  -10.2469150655 & -0.08 x_{14} & -0.10 x_{11} & -0.11 x_{3} & -0.76 x_{4} & -0.05 x_{17} & -0.09 x_{12} & -0.01 x_{13} & -1.38 x_{8} & -2.15 x_{9}\\
\end{array}\]
Primal Dictionary with original objective is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  1.98112948132 & -0.34 x_{14} & -0.41 x_{11} & +  3.90 x_{3} & +  2.33 x_{4} & -0.35 x_{17} & -0.78 x_{12} & +  0.09 x_{13} & -8.92 x_{8} & -10.14 x_{9}\\
 x_{2}   &  1.44323376757 & -0.00 x_{14} & +  0.11 x_{11} & +  0.45 x_{3} & -0.74 x_{4} & +  0.03 x_{17} & -0.05 x_{12} & -0.01 x_{13} & -0.92 x_{8} & +  1.41 x_{9}\\
 x_{6}   &  1.68076513251 & -0.02 x_{14} & -0.02 x_{11} & +  0.01 x_{3} & +  0.18 x_{4} & -0.04 x_{17} & +  0.05 x_{12} & -0.04 x_{13} & +  0.13 x_{8} & -0.29 x_{9}\\
 x_{7}   &  2.61129825044 & -0.02 x_{14} & -0.02 x_{11} & -0.36 x_{3} & -0.25 x_{4} & +  0.04 x_{17} & +  0.05 x_{12} & +  0.02 x_{13} & +  1.04 x_{8} & -0.32 x_{9}\\
 x_{1}   &  2.58483140274 & +  0.07 x_{14} & +  0.07 x_{11} & -0.23 x_{3} & +  0.02 x_{4} & -0.01 x_{17} & +  0.01 x_{12} & +  0.08 x_{13} & -0.07 x_{8} & +  0.28 x_{9}\\
 x_{15}   &  13.2464510363 & -0.87 x_{14} & -0.36 x_{11} & -2.16 x_{3} & +  0.06 x_{4} & -0.20 x_{17} & +  0.48 x_{12} & -0.80 x_{13} & +  1.92 x_{8} & +  0.68 x_{9}\\
 x_{16}   &  14.2299178497 & +  0.96 x_{14} & +  0.46 x_{11} & -5.29 x_{3} & +  4.61 x_{4} & -0.03 x_{17} & +  0.04 x_{12} & +  0.14 x_{13} & -9.94 x_{8} & -0.54 x_{9}\\
 x_{5}   &  1.92678651222 & +  0.05 x_{14} & -0.03 x_{11} & -0.76 x_{3} & +  0.54 x_{4} & +  0.04 x_{17} & +  0.02 x_{12} & -0.03 x_{13} & +  0.19 x_{8} & +  0.06 x_{9}\\
\hline
z    &  12.9223180834 & +  0.00 x_{14} & +  0.38 x_{11} & -4.69 x_{3} & +  1.09 x_{4} & +  0.22 x_{17} & -0.07 x_{12} & -0.05 x_{13} & -6.39 x_{8} & +  7.08 x_{9}\\
\end{array}\]
\section{Optimization Phase Simplex}
Starting Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  1.98112948132 & -0.34 x_{14} & -0.41 x_{11} & +  3.90 x_{3} & +  2.33 x_{4} & -0.35 x_{17} & -0.78 x_{12} & +  0.09 x_{13} & -8.92 x_{8} & -10.14 x_{9}\\
 x_{2}   &  1.44323376757 & -0.00 x_{14} & +  0.11 x_{11} & +  0.45 x_{3} & -0.74 x_{4} & +  0.03 x_{17} & -0.05 x_{12} & -0.01 x_{13} & -0.92 x_{8} & +  1.41 x_{9}\\
 x_{6}   &  1.68076513251 & -0.02 x_{14} & -0.02 x_{11} & +  0.01 x_{3} & +  0.18 x_{4} & -0.04 x_{17} & +  0.05 x_{12} & -0.04 x_{13} & +  0.13 x_{8} & -0.29 x_{9}\\
 x_{7}   &  2.61129825044 & -0.02 x_{14} & -0.02 x_{11} & -0.36 x_{3} & -0.25 x_{4} & +  0.04 x_{17} & +  0.05 x_{12} & +  0.02 x_{13} & +  1.04 x_{8} & -0.32 x_{9}\\
 x_{1}   &  2.58483140274 & +  0.07 x_{14} & +  0.07 x_{11} & -0.23 x_{3} & +  0.02 x_{4} & -0.01 x_{17} & +  0.01 x_{12} & +  0.08 x_{13} & -0.07 x_{8} & +  0.28 x_{9}\\
 x_{15}   &  13.2464510363 & -0.87 x_{14} & -0.36 x_{11} & -2.16 x_{3} & +  0.06 x_{4} & -0.20 x_{17} & +  0.48 x_{12} & -0.80 x_{13} & +  1.92 x_{8} & +  0.68 x_{9}\\
 x_{16}   &  14.2299178497 & +  0.96 x_{14} & +  0.46 x_{11} & -5.29 x_{3} & +  4.61 x_{4} & -0.03 x_{17} & +  0.04 x_{12} & +  0.14 x_{13} & -9.94 x_{8} & -0.54 x_{9}\\
 x_{5}   &  1.92678651222 & +  0.05 x_{14} & -0.03 x_{11} & -0.76 x_{3} & +  0.54 x_{4} & +  0.04 x_{17} & +  0.02 x_{12} & -0.03 x_{13} & +  0.19 x_{8} & +  0.06 x_{9}\\
\hline
z    &  12.9223180834 & +  0.00 x_{14} & +  0.38 x_{11} & -4.69 x_{3} & +  1.09 x_{4} & +  0.22 x_{17} & -0.07 x_{12} & -0.05 x_{13} & -6.39 x_{8} & +  7.08 x_{9}\\
\end{array}\]


 $ x_{4} $ enters and $ x_{2} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  6.53022942284 & -0.35 x_{14} & -0.05 x_{11} & +  5.31 x_{3} & -3.15 x_{2} & -0.26 x_{17} & -0.93 x_{12} & +  0.04 x_{13} & -11.81 x_{8} & -5.69 x_{9}\\
 x_{4}   &  1.95197694149 & -0.00 x_{14} & +  0.15 x_{11} & +  0.61 x_{3} & -1.35 x_{2} & +  0.04 x_{17} & -0.06 x_{12} & -0.02 x_{13} & -1.24 x_{8} & +  1.91 x_{9}\\
 x_{6}   &  2.02334906209 & -0.02 x_{14} & +  0.01 x_{11} & +  0.12 x_{3} & -0.24 x_{2} & -0.04 x_{17} & +  0.04 x_{12} & -0.04 x_{13} & -0.08 x_{8} & +  0.05 x_{9}\\
 x_{7}   &  2.13241207782 & -0.01 x_{14} & -0.06 x_{11} & -0.51 x_{3} & +  0.33 x_{2} & +  0.03 x_{17} & +  0.06 x_{12} & +  0.02 x_{13} & +  1.34 x_{8} & -0.79 x_{9}\\
 x_{1}   &  2.63035494293 & +  0.07 x_{14} & +  0.07 x_{11} & -0.22 x_{3} & -0.03 x_{2} & -0.01 x_{17} & +  0.01 x_{12} & +  0.08 x_{13} & -0.10 x_{8} & +  0.32 x_{9}\\
 x_{15}   &  13.3700053462 & -0.87 x_{14} & -0.35 x_{11} & -2.13 x_{3} & -0.09 x_{2} & -0.20 x_{17} & +  0.47 x_{12} & -0.80 x_{13} & +  1.85 x_{8} & +  0.80 x_{9}\\
 x_{16}   &  23.21905581 & +  0.94 x_{14} & +  1.17 x_{11} & -2.50 x_{3} & -6.23 x_{2} & +  0.14 x_{17} & -0.25 x_{12} & +  0.06 x_{13} & -15.65 x_{8} & +  8.27 x_{9}\\
 x_{5}   &  2.98449594384 & +  0.04 x_{14} & +  0.05 x_{11} & -0.43 x_{3} & -0.73 x_{2} & +  0.06 x_{17} & -0.01 x_{12} & -0.04 x_{13} & -0.48 x_{8} & +  1.10 x_{9}\\
\hline
z    &  15.0572278655 & -0.00 x_{14} & +  0.54 x_{11} & -4.02 x_{3} & -1.48 x_{2} & +  0.26 x_{17} & -0.14 x_{12} & -0.07 x_{13} & -7.75 x_{8} & +  9.18 x_{9}\\
\end{array}\]


 $ x_{9} $ enters and $ x_{10} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{9}   &  1.14832678654 & -0.06 x_{14} & -0.01 x_{11} & +  0.93 x_{3} & -0.55 x_{2} & -0.05 x_{17} & -0.16 x_{12} & +  0.01 x_{13} & -2.08 x_{8} & -0.18 x_{10}\\
 x_{4}   &  4.14778723804 & -0.12 x_{14} & +  0.14 x_{11} & +  2.39 x_{3} & -2.41 x_{2} & -0.05 x_{17} & -0.38 x_{12} & -0.00 x_{13} & -5.21 x_{8} & -0.34 x_{10}\\
 x_{6}   &  2.07515869675 & -0.02 x_{14} & +  0.01 x_{11} & +  0.16 x_{3} & -0.26 x_{2} & -0.04 x_{17} & +  0.03 x_{12} & -0.04 x_{13} & -0.18 x_{8} & -0.01 x_{10}\\
 x_{7}   &  1.23045465136 & +  0.03 x_{14} & -0.05 x_{11} & -1.24 x_{3} & +  0.77 x_{2} & +  0.06 x_{17} & +  0.19 x_{12} & +  0.02 x_{13} & +  2.98 x_{8} & +  0.14 x_{10}\\
 x_{1}   &  3.00191090092 & +  0.05 x_{14} & +  0.07 x_{11} & +  0.08 x_{3} & -0.21 x_{2} & -0.02 x_{17} & -0.04 x_{12} & +  0.08 x_{13} & -0.78 x_{8} & -0.06 x_{10}\\
 x_{15}   &  14.2870438874 & -0.92 x_{14} & -0.36 x_{11} & -1.38 x_{3} & -0.53 x_{2} & -0.24 x_{17} & +  0.34 x_{12} & -0.80 x_{13} & +  0.19 x_{8} & -0.14 x_{10}\\
 x_{16}   &  32.7122571521 & +  0.43 x_{14} & +  1.09 x_{11} & +  5.22 x_{3} & -10.81 x_{2} & -0.25 x_{17} & -1.60 x_{12} & +  0.12 x_{13} & -32.82 x_{8} & -1.45 x_{10}\\
 x_{5}   &  4.24589105208 & -0.02 x_{14} & +  0.04 x_{11} & +  0.60 x_{3} & -1.34 x_{2} & +  0.01 x_{17} & -0.19 x_{12} & -0.03 x_{13} & -2.76 x_{8} & -0.19 x_{10}\\
\hline
z    &  25.59460288 & -0.57 x_{14} & +  0.46 x_{11} & +  4.55 x_{3} & -6.57 x_{2} & -0.17 x_{17} & -1.64 x_{12} & +  0.00 x_{13} & -26.80 x_{8} & -1.61 x_{10}\\
\end{array}\]


 $ x_{3} $ enters and $ x_{7} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{9}   &  2.07404537453 & -0.04 x_{14} & -0.05 x_{11} & -0.75 x_{7} & +  0.02 x_{2} & +  0.00 x_{17} & -0.02 x_{12} & +  0.02 x_{13} & +  0.16 x_{8} & -0.07 x_{10}\\
 x_{4}   &  6.51822878107 & -0.06 x_{14} & +  0.03 x_{11} & -1.93 x_{7} & -0.93 x_{2} & +  0.07 x_{17} & -0.01 x_{12} & +  0.03 x_{13} & +  0.52 x_{8} & -0.07 x_{10}\\
 x_{6}   &  2.23664840498 & -0.02 x_{14} & -0.00 x_{11} & -0.13 x_{7} & -0.16 x_{2} & -0.03 x_{17} & +  0.06 x_{12} & -0.04 x_{13} & +  0.21 x_{8} & +  0.01 x_{10}\\
 x_{3}   &  0.990505568991 & +  0.03 x_{14} & -0.04 x_{11} & -0.80 x_{7} & +  0.62 x_{2} & +  0.05 x_{17} & +  0.15 x_{12} & +  0.01 x_{13} & +  2.40 x_{8} & +  0.11 x_{10}\\
 x_{1}   &  3.08533800569 & +  0.05 x_{14} & +  0.06 x_{11} & -0.07 x_{7} & -0.16 x_{2} & -0.02 x_{17} & -0.03 x_{12} & +  0.08 x_{13} & -0.57 x_{8} & -0.05 x_{10}\\
 x_{15}   &  12.9200960795 & -0.96 x_{14} & -0.30 x_{11} & +  1.11 x_{7} & -1.38 x_{2} & -0.31 x_{17} & +  0.13 x_{12} & -0.81 x_{13} & -3.12 x_{8} & -0.29 x_{10}\\
 x_{16}   &  37.8867660366 & +  0.58 x_{14} & +  0.87 x_{11} & -4.21 x_{7} & -7.58 x_{2} & +  0.02 x_{17} & -0.79 x_{12} & +  0.19 x_{13} & -20.30 x_{8} & -0.87 x_{10}\\
 x_{5}   &  4.83665827616 & -0.01 x_{14} & +  0.01 x_{11} & -0.48 x_{7} & -0.97 x_{2} & +  0.04 x_{17} & -0.10 x_{12} & -0.03 x_{13} & -1.33 x_{8} & -0.13 x_{10}\\
\hline
z    &  30.1051363046 & -0.44 x_{14} & +  0.27 x_{11} & -3.67 x_{7} & -3.75 x_{2} & +  0.06 x_{17} & -0.93 x_{12} & +  0.06 x_{13} & -15.89 x_{8} & -1.11 x_{10}\\
\end{array}\]


 $ x_{11} $ enters and $ x_{3} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{9}   &  0.939341421144 & -0.07 x_{14} & +  1.15 x_{3} & +  0.17 x_{7} & -0.68 x_{2} & -0.06 x_{17} & -0.20 x_{12} & +  0.01 x_{13} & -2.58 x_{8} & -0.20 x_{10}\\
 x_{4}   &  7.32104756403 & -0.03 x_{14} & -0.81 x_{3} & -2.58 x_{7} & -0.43 x_{2} & +  0.11 x_{17} & +  0.12 x_{12} & +  0.04 x_{13} & +  2.46 x_{8} & +  0.02 x_{10}\\
 x_{6}   &  2.23092624687 & -0.02 x_{14} & +  0.01 x_{3} & -0.13 x_{7} & -0.17 x_{2} & -0.03 x_{17} & +  0.06 x_{12} & -0.04 x_{13} & +  0.20 x_{8} & +  0.01 x_{10}\\
 x_{11}   &  23.1873290969 & +  0.65 x_{14} & -23.41 x_{3} & -18.84 x_{7} & + 14.46 x_{2} & +  1.18 x_{17} & +  3.62 x_{12} & +  0.30 x_{13} & + 56.08 x_{8} & +  2.60 x_{10}\\
 x_{1}   &  4.54906605045 & +  0.09 x_{14} & -1.48 x_{3} & -1.26 x_{7} & +  0.75 x_{2} & +  0.06 x_{17} & +  0.20 x_{12} & +  0.10 x_{13} & +  2.97 x_{8} & +  0.12 x_{10}\\
 x_{15}   &  5.95222414789 & -1.15 x_{14} & +  7.03 x_{3} & +  6.77 x_{7} & -5.72 x_{2} & -0.66 x_{17} & -0.96 x_{12} & -0.90 x_{13} & -19.97 x_{8} & -1.08 x_{10}\\
 x_{16}   &  58.0762564991 & +  1.14 x_{14} & -20.38 x_{3} & -20.61 x_{7} & +  5.00 x_{2} & +  1.04 x_{17} & +  2.36 x_{12} & +  0.45 x_{13} & + 28.53 x_{8} & +  1.39 x_{10}\\
 x_{5}   &  5.14737146158 & +  0.00 x_{14} & -0.31 x_{3} & -0.73 x_{7} & -0.78 x_{2} & +  0.05 x_{17} & -0.05 x_{12} & -0.02 x_{13} & -0.58 x_{8} & -0.09 x_{10}\\
\hline
z    &  36.31024456 & -0.27 x_{14} & -6.26 x_{3} & -8.71 x_{7} & +  0.12 x_{2} & +  0.38 x_{17} & +  0.04 x_{12} & +  0.14 x_{13} & -0.89 x_{8} & -0.41 x_{10}\\
\end{array}\]


 $ x_{2} $ enters and $ x_{15} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{9}   &  0.227582796827 & +  0.07 x_{14} & +  0.30 x_{3} & -0.64 x_{7} & +  0.12 x_{15} & +  0.02 x_{17} & -0.08 x_{12} & +  0.11 x_{13} & -0.19 x_{8} & -0.07 x_{10}\\
 x_{4}   &  6.86992673919 & +  0.05 x_{14} & -1.34 x_{3} & -3.09 x_{7} & +  0.08 x_{15} & +  0.16 x_{17} & +  0.19 x_{12} & +  0.11 x_{13} & +  3.98 x_{8} & +  0.10 x_{10}\\
 x_{6}   &  2.05910311005 & +  0.01 x_{14} & -0.20 x_{3} & -0.32 x_{7} & +  0.03 x_{15} & -0.01 x_{17} & +  0.08 x_{12} & -0.01 x_{13} & +  0.78 x_{8} & +  0.04 x_{10}\\
 x_{11}   &  38.2183898767 & -2.27 x_{14} & -5.65 x_{3} & -1.74 x_{7} & -2.53 x_{15} & -0.49 x_{17} & +  1.20 x_{12} & -1.98 x_{13} & +  5.65 x_{8} & -0.11 x_{10}\\
 x_{1}   &  5.33274132677 & -0.06 x_{14} & -0.55 x_{3} & -0.37 x_{7} & -0.13 x_{15} & -0.03 x_{17} & +  0.07 x_{12} & -0.02 x_{13} & +  0.34 x_{8} & -0.02 x_{10}\\
 x_{2}   &  1.03970816767 & -0.20 x_{14} & +  1.23 x_{3} & +  1.18 x_{7} & -0.17 x_{15} & -0.12 x_{17} & -0.17 x_{12} & -0.16 x_{13} & -3.49 x_{8} & -0.19 x_{10}\\
 x_{16}   &  63.2784011786 & +  0.13 x_{14} & -14.23 x_{3} & -14.69 x_{7} & -0.87 x_{15} & +  0.47 x_{17} & +  1.52 x_{12} & -0.34 x_{13} & + 11.08 x_{8} & +  0.45 x_{10}\\
 x_{5}   &  4.33674746211 & +  0.16 x_{14} & -1.27 x_{3} & -1.66 x_{7} & +  0.14 x_{15} & +  0.14 x_{17} & +  0.08 x_{12} & +  0.10 x_{13} & +  2.14 x_{8} & +  0.05 x_{10}\\
\hline
z    &  36.4304526832 & -0.29 x_{14} & -6.12 x_{3} & -8.57 x_{7} & -0.02 x_{15} & +  0.37 x_{17} & +  0.02 x_{12} & +  0.12 x_{13} & -1.29 x_{8} & -0.43 x_{10}\\
\end{array}\]


 $ x_{12} $ enters and $ x_{9} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{12}   &  2.79224959762 & +  0.86 x_{14} & +  3.73 x_{3} & -7.85 x_{7} & +  1.47 x_{15} & +  0.27 x_{17} & -12.27 x_{9} & +  1.39 x_{13} & -2.38 x_{8} & -0.87 x_{10}\\
 x_{4}   &  7.40650406504 & +  0.22 x_{14} & -0.63 x_{3} & -4.60 x_{7} & +  0.36 x_{15} & +  0.21 x_{17} & -2.36 x_{9} & +  0.37 x_{13} & +  3.52 x_{8} & -0.07 x_{10}\\
 x_{6}   &  2.29619082993 & +  0.09 x_{14} & +  0.12 x_{3} & -0.99 x_{7} & +  0.15 x_{15} & +  0.01 x_{17} & -1.04 x_{9} & +  0.10 x_{13} & +  0.57 x_{8} & -0.03 x_{10}\\
 x_{11}   &  41.575543725 & -1.23 x_{14} & -1.15 x_{3} & -11.18 x_{7} & -0.76 x_{15} & -0.17 x_{17} & -14.75 x_{9} & -0.31 x_{13} & +  2.78 x_{8} & -1.16 x_{10}\\
 x_{1}   &  5.54145516074 & +  0.01 x_{14} & -0.27 x_{3} & -0.95 x_{7} & -0.02 x_{15} & -0.01 x_{17} & -0.92 x_{9} & +  0.08 x_{13} & +  0.16 x_{8} & -0.09 x_{10}\\
 x_{2}   &  0.573356444224 & -0.35 x_{14} & +  0.61 x_{3} & +  2.49 x_{7} & -0.42 x_{15} & -0.16 x_{17} & +  2.05 x_{9} & -0.39 x_{13} & -3.09 x_{8} & -0.04 x_{10}\\
 x_{16}   &  67.5360901325 & +  1.45 x_{14} & -8.54 x_{3} & -26.67 x_{7} & +  1.36 x_{15} & +  0.87 x_{17} & -18.71 x_{9} & +  1.78 x_{13} & +  7.45 x_{8} & -0.87 x_{10}\\
 x_{5}   &  4.55565185093 & +  0.23 x_{14} & -0.98 x_{3} & -2.27 x_{7} & +  0.25 x_{15} & +  0.17 x_{17} & -0.96 x_{9} & +  0.21 x_{13} & +  1.95 x_{8} & -0.01 x_{10}\\
\hline
z    &  36.475093888 & -0.28 x_{14} & -6.06 x_{3} & -8.70 x_{7} & +  0.00 x_{15} & +  0.37 x_{17} & -0.20 x_{9} & +  0.15 x_{13} & -1.33 x_{8} & -0.45 x_{10}\\
\end{array}\]


 $ x_{13} $ enters and $ x_{2} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{12}   &  4.83550333439 & -0.37 x_{14} & +  5.89 x_{3} & +  1.04 x_{7} & -0.03 x_{15} & -0.30 x_{17} & -4.97 x_{9} & -3.56 x_{2} & -13.40 x_{8} & -1.02 x_{10}\\
 x_{4}   &  7.95649412512 & -0.11 x_{14} & -0.05 x_{3} & -2.21 x_{7} & -0.04 x_{15} & +  0.06 x_{17} & -0.39 x_{9} & -0.96 x_{2} & +  0.56 x_{8} & -0.11 x_{10}\\
 x_{6}   &  2.44998412194 & -0.01 x_{14} & +  0.28 x_{3} & -0.32 x_{7} & +  0.04 x_{15} & -0.03 x_{17} & -0.49 x_{9} & -0.27 x_{2} & -0.26 x_{8} & -0.04 x_{10}\\
 x_{11}   &  41.1162273738 & -0.95 x_{14} & -1.64 x_{3} & -13.18 x_{7} & -0.43 x_{15} & -0.04 x_{17} & -16.39 x_{9} & +  0.80 x_{2} & +  5.26 x_{8} & -1.12 x_{10}\\
 x_{1}   &  5.66338520165 & -0.07 x_{14} & -0.14 x_{3} & -0.42 x_{7} & -0.11 x_{15} & -0.05 x_{17} & -0.48 x_{9} & -0.21 x_{2} & -0.50 x_{8} & -0.10 x_{10}\\
 x_{13}   &  1.47062559543 & -0.89 x_{14} & +  1.55 x_{3} & +  6.40 x_{7} & -1.08 x_{15} & -0.41 x_{17} & +  5.26 x_{9} & -2.56 x_{2} & -7.93 x_{8} & -0.11 x_{10}\\
 x_{16}   &  70.1530644649 & -0.13 x_{14} & -5.78 x_{3} & -15.28 x_{7} & -0.55 x_{15} & +  0.14 x_{17} & -9.36 x_{9} & -4.56 x_{2} & -6.66 x_{8} & -1.07 x_{10}\\
 x_{5}   &  4.86281359162 & +  0.04 x_{14} & -0.65 x_{3} & -0.93 x_{7} & +  0.03 x_{15} & +  0.08 x_{17} & +  0.14 x_{9} & -0.54 x_{2} & +  0.30 x_{8} & -0.04 x_{10}\\
\hline
z    &  36.6887900921 & -0.41 x_{14} & -5.84 x_{3} & -7.77 x_{7} & -0.15 x_{15} & +  0.31 x_{17} & +  0.57 x_{9} & -0.37 x_{2} & -2.48 x_{8} & -0.46 x_{10}\\
\end{array}\]


 $ x_{9} $ enters and $ x_{12} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{9}   &  0.973593350384 & -0.07 x_{14} & +  1.19 x_{3} & +  0.21 x_{7} & -0.01 x_{15} & -0.06 x_{17} & -0.20 x_{12} & -0.72 x_{2} & -2.70 x_{8} & -0.21 x_{10}\\
 x_{4}   &  7.5747655584 & -0.08 x_{14} & -0.51 x_{3} & -2.29 x_{7} & -0.04 x_{15} & +  0.08 x_{17} & +  0.08 x_{12} & -0.68 x_{2} & +  1.61 x_{8} & -0.03 x_{10}\\
 x_{6}   &  1.97086530264 & +  0.03 x_{14} & -0.30 x_{3} & -0.42 x_{7} & +  0.04 x_{15} & -0.00 x_{17} & +  0.10 x_{12} & +  0.08 x_{2} & +  1.07 x_{8} & +  0.06 x_{10}\\
 x_{11}   &  25.1561807332 & +  0.27 x_{14} & -21.08 x_{3} & -16.60 x_{7} & -0.33 x_{15} & +  0.96 x_{17} & +  3.30 x_{12} & + 12.56 x_{2} & + 49.48 x_{8} & +  2.25 x_{10}\\
 x_{1}   &  5.19477834612 & -0.03 x_{14} & -0.71 x_{3} & -0.52 x_{7} & -0.11 x_{15} & -0.02 x_{17} & +  0.10 x_{12} & +  0.13 x_{2} & +  0.80 x_{8} & +  0.00 x_{10}\\
 x_{13}   &  6.58778772379 & -1.28 x_{14} & +  7.79 x_{3} & +  7.50 x_{7} & -1.11 x_{15} & -0.73 x_{17} & -1.06 x_{12} & -6.34 x_{2} & -22.10 x_{8} & -1.19 x_{10}\\
 x_{16}   &  61.0447570332 & +  0.57 x_{14} & -16.87 x_{3} & -17.24 x_{7} & -0.50 x_{15} & +  0.71 x_{17} & +  1.88 x_{12} & +  2.15 x_{2} & + 18.57 x_{8} & +  0.86 x_{10}\\
 x_{5}   &  4.99514066496 & +  0.03 x_{14} & -0.49 x_{3} & -0.91 x_{7} & +  0.03 x_{15} & +  0.07 x_{17} & -0.03 x_{12} & -0.63 x_{2} & -0.07 x_{8} & -0.06 x_{10}\\
\hline
z    &  37.2413895993 & -0.45 x_{14} & -5.16 x_{3} & -7.65 x_{7} & -0.16 x_{15} & +  0.28 x_{17} & -0.11 x_{12} & -0.78 x_{2} & -4.01 x_{8} & -0.58 x_{10}\\
\end{array}\]


 $ x_{17} $ enters and $ x_{13} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{9}   &  0.42451511445 & +  0.03 x_{14} & +  0.54 x_{3} & -0.42 x_{7} & +  0.09 x_{15} & +  0.08 x_{13} & -0.11 x_{12} & -0.19 x_{2} & -0.85 x_{8} & -0.11 x_{10}\\
 x_{4}   &  8.30840468286 & -0.23 x_{14} & +  0.36 x_{3} & -1.46 x_{7} & -0.17 x_{15} & -0.11 x_{13} & -0.04 x_{12} & -1.38 x_{2} & -0.85 x_{8} & -0.16 x_{10}\\
 x_{6}   &  1.93901799755 & +  0.04 x_{14} & -0.34 x_{3} & -0.46 x_{7} & +  0.05 x_{15} & +  0.00 x_{13} & +  0.10 x_{12} & +  0.12 x_{2} & +  1.18 x_{8} & +  0.06 x_{10}\\
 x_{11}   &  33.8017648087 & -1.41 x_{14} & -10.86 x_{3} & -6.77 x_{7} & -1.78 x_{15} & -1.31 x_{13} & +  1.91 x_{12} & +  4.25 x_{2} & + 20.47 x_{8} & +  0.68 x_{10}\\
 x_{1}   &  5.04551808492 & -0.00 x_{14} & -0.89 x_{3} & -0.69 x_{7} & -0.08 x_{15} & +  0.02 x_{13} & +  0.12 x_{12} & +  0.28 x_{2} & +  1.30 x_{8} & +  0.03 x_{10}\\
 x_{17}   &  9.00165996855 & -1.75 x_{14} & + 10.64 x_{3} & + 10.24 x_{7} & -1.51 x_{15} & -1.37 x_{13} & -1.45 x_{12} & -8.66 x_{2} & -30.20 x_{8} & -1.63 x_{10}\\
 x_{16}   &  67.467936397 & -0.68 x_{14} & -9.28 x_{3} & -9.93 x_{7} & -1.58 x_{15} & -0.98 x_{13} & +  0.85 x_{12} & -4.03 x_{2} & -2.98 x_{8} & -0.30 x_{10}\\
 x_{5}   &  5.63515638651 & -0.09 x_{14} & +  0.26 x_{3} & -0.18 x_{7} & -0.08 x_{15} & -0.10 x_{13} & -0.13 x_{12} & -1.25 x_{2} & -2.22 x_{8} & -0.18 x_{10}\\
\hline
z    &  39.7178053468 & -0.93 x_{14} & -2.24 x_{3} & -4.83 x_{7} & -0.57 x_{15} & -0.38 x_{13} & -0.51 x_{12} & -3.16 x_{2} & -12.32 x_{8} & -1.03 x_{10}\\
\end{array}\]
Final Dictionary
Solution:  39.7178053468
Num Pivots:  10
\end{document}
